Question

2. Find the magnitude and direction of the resultant vector of two forces. The first force is 250 pounds at an angle of 25 degrees with the horizontal and the second force is 45 pounds at an angle of 250 degrees with the horizontal.

Answer 1

Answer:

Magnitude = 220.49pounds

Direction = 16.7°

Step-by-step explanation:

Find attached the diagram obtained from the given information.

From the diagram, 25° is in the first quadrant with all positive values: x = cos25°, y = sin35°

Force for the x and y component: Fx, Fy

250(sin25, cos25) = (250sin25, 250cos25)

= [250(0.4226), 250(0.9063)]

= (105.65, 226.575)

The 250° is in the 2nd quadrant with values: x = cos250°, y = sin250°

Force for the x and y component: (Fx, Fy)

45(sin250, cos250) = (45sin250, 45cos250) = [45(-0.9397), 45(-0.3420]

= (−42.2865, -15.39)

The resultant forces for x and y components = sum of Fx in the 1st and 2nd force and, sum of Fy in the 1st and 2nd force

sum of Fx in the 1st and 2nd force = 105.65 + (−42.2865) = 63.3635

sum of Fy in the 1st and 2nd force = 226.575 + (-15.39) = 211.185

Magnitude = √[(ΣFx)² + (ΣFy)²]

= √[(63.3635)² + (211.185)²]

= √(4014.9331 + 44599.1042)

= √(48614.0373)

= 220.49pounds

Direction = arctan (ΣFx/ΣFy)

= arctan (63.3635/211.185)

= arctan(0.30)

= 16.7°